%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL390+1 : TPTP v9.2.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:40:12 PM UTC 2026
% Result : Theorem 11.52s 8.07s
% Output : CNFRefutation 11.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 37 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 49 ~; 44 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 163 ( 38 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(cn_1,axiom,
! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(cn_3,axiom,
! [X1,X2] : is_a_theorem(implies(X1,implies(not(X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(cn_2,axiom,
! [X1] : is_a_theorem(implies(implies(not(X1),X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(prove_cn_53,conjecture,
is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_53) ).
fof(c_0_5,plain,
! [X12,X13] :
( ~ is_a_theorem(implies(X12,X13))
| ~ is_a_theorem(X12)
| is_a_theorem(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[condensed_detachment])]) ).
fof(c_0_6,plain,
! [X14,X15,X16] : is_a_theorem(implies(implies(X14,X15),implies(implies(X15,X16),implies(X14,X16)))),
inference(variable_rename,[status(thm)],[cn_1]) ).
cnf(c_0_7,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_10,plain,
! [X18,X19] : is_a_theorem(implies(X18,implies(not(X18),X19))),
inference(variable_rename,[status(thm)],[cn_3]) ).
cnf(c_0_11,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_12,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X17] : is_a_theorem(implies(implies(not(X17),X17),X17)),
inference(variable_rename,[status(thm)],[cn_2]) ).
cnf(c_0_14,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,implies(X4,X3)))
| ~ is_a_theorem(implies(X2,X4)) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_17,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_18,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_19,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_20,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_21,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(X4,X2))
| ~ is_a_theorem(implies(X1,X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_22,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(implies(not(X1),X4),X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1)),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),not(X1))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_26,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_9]) ).
cnf(c_0_27,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(implies(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(not(implies(implies(not(X1),X1),X1)),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(X4,X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_33,plain,
( is_a_theorem(implies(implies(not(X1),X1),implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_34,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
| ~ is_a_theorem(implies(not(implies(X1,X3)),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_8]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X4,X3))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(implies(not(X1),X1),X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_39,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(X3),X4)))
| ~ is_a_theorem(implies(implies(implies(X2,X5),implies(X1,X5)),X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_15]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3))))
| ~ is_a_theorem(implies(X1,implies(X4,X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(not(X3),X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_15]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(not(implies(X1,X1)),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_12]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(X1,implies(not(implies(not(X1),X2)),X3))),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_46,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(not(X3),X3)))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_38]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(implies(X2,X1),X1)),X3))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X3)))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(not(implies(X1,implies(not(X1),X2))),X3)),
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(implies(not(X1),X2),X3))
| ~ is_a_theorem(implies(implies(implies(X2,X1),X1),X3)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_24,c_0_50]) ).
fof(c_0_54,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_cn_53])]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_19,c_0_47]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),X3)))
| ~ is_a_theorem(implies(X1,implies(not(X3),X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_55]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X1)),X3))),
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(implies(not(not(X1)),X2),X1),X1)),
inference(spm,[status(thm)],[c_0_19,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),y),implies(not(y),x))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
( is_a_theorem(implies(implies(not(X1),X2),implies(X3,X1)))
| ~ is_a_theorem(implies(X3,implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_55]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_60]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(implies(not(X1),not(not(X1))),X1)),
inference(spm,[status(thm)],[c_0_51,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
~ is_a_theorem(implies(not(y),implies(y,x))),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
~ is_a_theorem(implies(y,not(not(y)))),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_24,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LCL390+1 : TPTP v9.2.1. Released v9.1.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 22:29:15 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 11.52/8.07 % Version : CSE_E---1.7
% 11.52/8.07 % Problem : theBenchmark.p
% 11.52/8.07 % SZS status Theorem for theBenchmark.p
% 11.52/8.07 % SZS output start CNFRefutation
% See solution above
% 11.62/8.11 % Total time : 6.367s
%------------------------------------------------------------------------------